HARTFORD — Gov. Dannel P. Malloy has presented his version of a new state budget, but now it's time for legislators, lobbyists and everyone else to have their say about its final form.

The process began Thursday with a presentation by the governor's budget director to the legislature's appropriations committee and continues Tuesday with eight days of often-intense public hearings.

Malloy's two-year, $40 billion proposal and the spending plans for more than 65 separate departments, commissions and agencies will be changed and molded like a chunk of Play-Doh as legislators finally get their hands on the document.

During the hearings, members of the public will generally have three minutes to make their case for changes. That timeframe can be extended if legislators have questions, and advocates may also submit detailed written testimony. The order of the speakers is chosen through a lottery, so some advocates can be frustrated if they get sent to the back of the line, said Sen. Beth Bye, a West Hartford Democrat who co-chairs the committee.

"I think it can be hard because you get three minutes and sometimes you wait hours to get your three minutes,'' Bye said. "Even the legislators go in the lottery. People are definitely heard. The chairs are usually in the room. The people who are making the decisions are in the room. I do think it makes a difference. Groups that have been really organized have done well in the budget.''

Bye said she's expecting to hear from the University of Connecticut, which is facing a projected cutback of $100 million over two years.

"I expect UConn students to come out if they're being taught about government and how it works,'' Bye said, adding that complaints started arriving in the first 24 hours after Malloy's speech. "I have already heard from parents who are concerned about tuition at UConn.''

Tuition is already expected to be increased at UConn by about 6.75 percent in the next academic year. The Malloy administration has said that UConn is a large operation with thousands of employees, millions of dollars in a fund balance and an annual budget of more than $1 billion.

Gov. Dannel P. Malloy presented his Biennial Budget plan Wednesday to the General Assembly in the Hall of the House at the state Capitol.

Budget director Ben Barnes accented some of the unknowns in the budget in his presentation to legislators. For instance, the state is expecting a 25 percent increase in the portion of the state income tax that includes capital gains on stocks. That would be generated by what has so far been a fairly well-sustained run-up on Wall Street.

"There's always uncertainty, and in the current economy, there's more uncertainty than normal,'' Barnes said. "We have billions of dollars, uncollected at this date, that we expect to collect in April. It could outpace our expectations."

Or it could fall short. Barnes said if the revenue increase is only 15 percent instead of 25 percent, the state could be short $150 million from what is expected.

House Speaker Brendan Sharkey said he believes the legislature will change one of Malloy's most publicized ideas — cutting the sales tax over two years while simultaneously making changes in other areas of taxation.

The plan calls for reducing the 6.35 percent sales tax to 6.2 percent in November and then down to 5.95 percent in April 2017. At the same time, Malloy says the state should continue charging sales tax on clothing and footwear items under $50, which would cost consumers $280 million over two years.

Sharkey questioned the maneuver in an attempt to initially shave a few percentage points off the sales tax.

"If you're going to make changes that involve a lot of painful choices on items that will be taxed or not taxed by the sales tax, to me, you have to come up with a big vision — a big goal — to warrant going through the pain of that,'' Sharkey said.

"If we're going to do something big, let's do that. But I'm not sure that four-tenths of 1 percent on the sales tax is necessarily that big idea that warrants that kind of attention and pain that we'd have to go through.''

Sharkey has closely followed taxes through the years and was co-chairman of the Program Review and Investigations Committee in 2005, when it conducted a study of the state's tax structure. He stressed that he was not foreclosing any options about taxes, but he said it will not be easy.